Bug Report: Melamine (CAS 108-78-1) — Tb is inconsistent; melamine sublimes, it has no stable liquid at 1 atm #180

Summary

thermo.Chemical('melamine') stores Tb = 704.0 K (430.9 °C), treating melamine as a normal solid→liquid→gas compound. In reality, melamine sublimes at its melting temperature (~618 K / 345 °C) under atmospheric pressure; no stable liquid phase exists at 1 atm.

The consequence: Chemical('melamine', T=663.15, P=360e3) returns phase='l' when the correct phase at relevant industrial operating conditions is gas.

A related symptom: the H(T) enthalpy curve shows two separate jumps (s→l at Tm + l→g at Tb) instead of the single jump expected for a subliming compound (s→g at ~Tm).

Environment

• thermo version: 0.6.0
• Python: 3.13.9

Reproducer

from thermo.chemical import Chemical

m = Chemical('melamine')
print(f'Tb: {m.Tb:.1f} K ({m.Tb-273.15:.1f} °C)')       # 704.0 K (430.9 °C)
print(f'Tm: {m.Tm:.1f} K ({m.Tm-273.15:.1f} °C)')       # 618.1 K (345.0 °C)

# Phase scan at 101.325 kPa — shows s→l→g (wrong for a subliming compound)
for Tc in [610, 618, 620, 630, 650, 663, 680, 698, 704, 720]:
    m3 = Chemical('melamine', T=Tc, P=101325)
    print(f'  T={Tc}K ({Tc-273.15:.0f}°C): phase={m3.phase}')
# Observed: s (610K) → l (620K) → g (698K)
# Expected for sublimation:  s (610K) → g (698K)    — no liquid phase at 1 atm

# Industrial operating conditions
m_op = Chemical('melamine', T=390+273.15, P=360e3)
print(f'Phase at 390°C / 360 kPa: {m_op.phase}')          # 'l' ← should be 'g'

Evidence 1: Hirt (1960) vapor pressure equation

The classic Hirt, Steger et al. (1960) paper (Journal of Polymer Science) experimentally measured melamine vapor pressure by Knudsen effusion and reported the correlation:

log₁₀(P) = 12.52 − 6440/T (P in mmHg, T in K)

This is the NIST reference for melamine vapor pressure and sublimation enthalpy.

The Hirt equation predicts sublimation, not liquid→gas

At thermo's stored Tm = 618 K, the sublimation vapor pressure is:

P_sub(Tm) = 10^(12.52 − 6440/618) = 126 mmHg = 16.8 kPa

This ~17 kPa is the triple-point pressure of melamine. At 1 atm (101 kPa) ≈ 6× the triple-point pressure, one might expect a stable liquid. However, melamine's high sublimation rate near its melting point means the liquid phase is practically non-existent at atmospheric conditions — the compound goes directly from solid to gas.

Cross-check against stored Tb

If Tb = 704 K is treated as a normal boiling point (where P_sat = 1 atm), the Hirt equation gives:

P(704K) = 10^(12.52 − 6440/704) = 10^3.372 = 2355 mmHg = 3.1 atm

→ At 704 K, the Hirt equation predicts P_sat = 3.1 atm, not 1 atm. The equation is an excellent fit for experimentally validated data (ΔH_sub = 123.2 kJ/mol from slope vs NIST 120±4 kJ/mol), so the error is in the stored Tb, not the equation.

Equation validation

(Note: Thermo also stores Joback-estimated Hsub = 951.5 kJ/mol and Hvap_Tb = 603.5 kJ/mol, which overestimate ~8× for the triazine ring; the m-suffixed properties are the correct literature values.)

Evidence 2: Industrial practice

The urea-to-melamine pyrolysis process operates at 380–400 °C and ~360 kPa, with melamine collected as a gas-phase product. At these conditions (T=390°C, P=360 kPa), Chemical('melamine') returns phase='l', contradicting industrial practice.

The phase misprediction has a significant enthalpy impact: the liquid-phase enthalpy at 390°C excludes the vaporization enthalpy (~92 kJ/mol from Hsubm − Hfusm), causing errors of ~1 GJ per tonne of melamine in reaction enthalpy calculations.

Evidence 3: H vs T enthalpy scan — two jumps instead of one

The H vs T scan at 1 atm reveals the problem visually: thermo produces two separate enthalpy jumps at the positions of Tm and Tb, when a subliming compound should show a single jump at the sublimation temperature.

The two jumps sum to 106.7 kJ/mol — close to the expected Hsub of 120 kJ/mol, but split incorrectly into melting + vaporization at the wrong temperatures. The 13 kJ/mol gap is due to the sensible heat of the spurious liquid phase that shouldn't exist at 1 atm.

import numpy as np
import matplotlib.pyplot as plt
from thermo.chemical import Chemical

species = 'melamine'
P = 101325  # Pa (1 atm)
T_min, T_max, N = 580, 730, 150

temps = np.linspace(T_min, T_max, N)
H_vals, phases = [], []
for T in temps:
    m = Chemical(species, T=T, P=P)
    H_vals.append(m.H)
    phases.append(m.phase)
H_vals = np.array(H_vals)

fig, ax = plt.subplots(figsize=(10, 5))
colors = {'s': '#4a90d9', 'l': '#e67e22', 'g': '#e74c3c'}
for ph in ('s', 'l', 'g'):
    mask = np.array(phases) == ph
    if mask.any():
        ax.scatter(temps[mask], H_vals[mask], c=colors[ph], s=8,
                   label={'s':'Solid','l':'Liquid','g':'Gas'}[ph])

m0 = Chemical(species)
for name, Tv in [('Tm', m0.Tm), ('Tb', m0.Tb)]:
    ax.axvline(Tv, color='#2c3e50', ls='--', lw=0.8, alpha=0.5)
    ax.text(Tv+3, ax.get_ylim()[1]*0.95, f'{name}={Tv:.0f}K', fontsize=8)

ax.set_xlabel('T (K)'); ax.set_ylabel('H (J/kg)')
ax.set_title(f'{species} — H vs T (P={P/101325:.2f} atm)')
ax.legend(); ax.grid(alpha=0.3)
fig.tight_layout()
fig.savefig('/tmp/melamine_H_vs_T.png', dpi=150)

Suggested Fix

Melamine should be treated as a subliming compound. At atmospheric pressure, it does not have a stable liquid phase. The Hsub and Tb parameters should be consistent with sublimation behavior.

1. Set Tb to match Tm (~618 K / 345 °C), since melamine sublimes at its melting temperature. The solid→gas transition temperature is ~618 K, not 704 K.
2. Alternatively, mark melamine as a subliming compound, so the s→l→g phase sequence is replaced by direct s→g.

Additionally: the inflated Joback-estimated values (Hsub = 951.5 kJ/mol, Hfus = 220.4 kJ/mol, Hvap_Tb = 603.5 kJ/mol) should be corrected to match the literature data already stored in the m-suffixed properties (Hsubm = 120.0, Hvapm = 127.3, Hfusm = 27.8).

References

1. Hirt, R. C., Steger, J. E., et al. Vapor Pressure of Melamine. Journal of Polymer Science, 1960.
   — Primary source of the vapor pressure correlation. Knudsen effusion, ΔsubH° = 120 ± 4 kJ/mol.

2. Stephenson, R. M., Malanowski, S. Handbook of the Thermodynamics of Organic Compounds. Elsevier, 1987.
   — ΔsubH° = 121.3 ± 4.2 kJ/mol.

3. Dorofeeva, O. V. Quantum-chemical study of gas-phase enthalpies of formation of urea-derived compounds. Struct. Chem. 28, 1541–1550 (2017). DOI: 10.1007/s11224-017-0937-4
   — QC-derived ΔsubH° ≈ 142 kJ/mol, same order of magnitude.

Reported from industrial chemical engineering context. Happy to provide additional validation data or participate in discussion.